Random initialization of coefficients

Oct 13, 2025 by windailys.com 136 views

Multinomial Lasso Producing Different LASSO Output Despite Using Seed: A Discussion on Lasso and Glmnet

In the realm of machine learning and statistical modeling, regularization techniques play a crucial role in preventing overfitting and improving the generalizability of models. One such technique is the Lasso (Least Absolute Shrinkage and Selection Operator), which has gained significant attention in recent years due to its ability to perform feature selection and shrinkage simultaneously. The multinomial Lasso, a variant of the Lasso, is particularly useful for multinomial logistic regression problems. However, users of the glmnet package in R have reported instances where the multinomial Lasso produces different output despite using a seed for reproducibility. In this article, we will delve into the world of Lasso and glmnet, exploring the reasons behind this phenomenon and providing insights on how to achieve reproducible results.

The Lasso is a regularization technique that adds a penalty term to the loss function, which is proportional to the absolute value of the coefficients. This penalty term encourages the model to shrink the coefficients of less important features to zero, effectively performing feature selection. The glmnet package in R provides an efficient implementation of the Lasso, as well as other regularization techniques such as elastic net and ridge regression.

The multinomial Lasso is a variant of the Lasso that is specifically designed for multinomial logistic regression problems. In this type of problem, the response variable has multiple categories, and the goal is to predict the probability of each category given the predictor variables. The multinomial Lasso uses a similar approach to the Lasso, but with a few key modifications to accommodate the multinomial response variable.

Despite using a seed for reproducibility, users of the glmnet package have reported instances where the multinomial Lasso produces different output. This can be frustrating, especially when working on complex projects that require precise and reproducible results. So, what could be causing this issue?

There are several reasons why the multinomial Lasso may produce different output despite using a seed for reproducibility. Some of these reasons include:

Random initialization of coefficients: In the glmnet package, the coefficients are initialized randomly, which can lead to different results even when using a seed.
Non-deterministic algorithm: The glmnet package uses a non-deterministic algorithm to solve the optimization problem, which can result in different solutions even when using a seed.
Numerical instability: The multinomial Lasso involves numerical computations, which can be prone to instability and lead to different results.

To achieve reproducibility with the multinomial Lasso, you can try the following solutions:

Use a fixed seed: Make sure to use a fixed seed for reproducibility. You can set the seed using the set.seed() function in R.
Use a deterministic algorithm: If possible, use a deterministic algorithm to solve the optimization problem. This can be achieved by setting the standardize argument to TRUE in the glmnet() function.
Use a more stable algorithm: Consider using a more stable algorithm, such as the cv.glmnet() function, which uses a more robust optimization algorithm.

Here is an example code snippet that demonstrates how to use the multinomial Lasso with reproducibility:

# Load the glmnet package
library(glmnet)
set.seed(123)
data(mtcars)
mtcars $am &lt;- factor(mtcars$ am, levels = c(0, 1))
fit <- glmnet(mtcars[, 1:10], mtcars$am, family = "multinomial", standardize = TRUE)
print(fit$beta)

In conclusion, the multinomial Lasso can produce different output despite using a seed for reproducibility due to various reasons such as random initialization of coefficients, non-deterministic algorithm, and numerical instability. However, by using a fixed seed, a deterministic algorithm, and a more stable algorithm, you can achieve reproducibility with the multinomial Lasso. We hope this article has provided valuable insights and solutions to help you overcome the challenges of non-reproducibility with the multinomial Lasso.

For further information on the multinomial Lasso and glmnet, we recommend the following resources:

glmnet package documentation: The glmnet package documentation provides detailed information on the multinomial Lasso and other regularization techniques.
R documentation: The R documentation provides information on the glmnet() function and other related functions.
Statistical learning with R: The book "Statistical Learning with R" by Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani provides a comprehensive introduction to statistical learning and regularization techniques.
Multinomial Lasso Q&A: Answers to Your Questions

In our previous article, we discussed the multinomial Lasso and its implementation in the glmnet package in R. We also explored the reasons behind non-reproducibility and provided solutions to achieve reproducibility. In this article, we will answer some of the most frequently asked questions about the multinomial Lasso and glmnet.

A: The multinomial Lasso is a variant of the Lasso that is specifically designed for multinomial logistic regression problems. It uses a similar approach to the Lasso, but with a few key modifications to accommodate the multinomial response variable.

A: The main difference between the multinomial Lasso and the Lasso is the type of response variable. The Lasso is designed for binary logistic regression problems, while the multinomial Lasso is designed for multinomial logistic regression problems.

A: To use the multinomial Lasso in glmnet, you can use the glmnet() function with the family argument set to "multinomial". For example:

fit <- glmnet(x, y, family = "multinomial")

A: The standardize argument in glmnet is used to standardize the predictor variables. When set to TRUE, glmnet standardizes the predictor variables by subtracting the mean and dividing by the standard deviation. This can help improve the stability of the model.

A: To achieve reproducibility with the multinomial Lasso, you can use a fixed seed, a deterministic algorithm, and a more stable algorithm. For example:

set.seed(123)
fit <- glmnet(x, y, family = "multinomial", standardize = TRUE)

A: The cv.glmnet() function in glmnet is used to perform cross-validation on the multinomial Lasso model. It returns a list of objects that contain the cross-validation results.

A: To use the cv.glmnet() function in glmnet, you can use the following code:

cv_fit <- cv.glmnet(x, y, family = "multinomial", standardize = TRUE)

A: The plot() function in glmnet is used to plot the cross-validation results. It returns a plot of the cross-validation error against the regularization parameter.

A: To use the plot() function in glmnet, you can use the following code:

plot(cv_fit)

In conclusion, the multinomial Lasso is a powerful tool for multinomial logistic regression problems. By using the glmnet package in R, you can easily implement the multinomial Lasso and achieve reproducibility. We hope this Q&A article has provided valuable insights and answers to your questions.

For further information on the multinomial Lasso and glmnet, we recommend the following resources:

glmnet package documentation: The glmnet package documentation provides detailed information on the multinomial Lasso and other regularization techniques.
R documentation: The R documentation provides information on the glmnet() function and other related functions.
Statistical learning with R: The book "Statistical Learning with R" by Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani provides a comprehensive introduction to statistical learning and regularization techniques.